In place of the dwelling on Main St, a new entranceway to the supermarket would be established, as would additional carparking.
The pylon sign would direct Main St traffic to the new parking area.
Ms Reid said the "character and charm" of the historic heritage precinct was "a major drawcard" for visitors and locals alike.
"Our aim is to protect it in order to attract customers to Greytown so businesses thrive."
Friends of Historic Greytown are appealing for funds to help with the legal proceedings, and rallying residents to speak out against the council's lack of public consultation.
The Wairarapa Combined District Plan states that within historic heritage precincts "no individual sign exceeds 2m2 in area".
It also says "no sign is illuminated by any means other than directional lighting", however, the proposed sign will be internally lit.
"All signs must be sympathetic in scale, colour and design with amenities and historical qualities of the area," the plan states.
Despite these regulations, the council approved the application, by General Distributors, as a "discretionary activity".
SWDC's acting chief executive Mark Allingham said: "After consideration of the proposal with the District Plan, including its heritage provisions, the development was considered appropriate relative to the zoning of the site and scale of the business."
The two resource consents were processed on a non-notified basis, meaning public notification was not required as the proposal's adverse effects were deemed to be less than minor on a community level.
Mr Allingham said the development would give the supermarket a Main St presence.
The proposal included the voluntary retention of a large copper beech tree on the site, which could otherwise have been removed, Mr Allingham said.
However, Friends of Historic Greytown are concerned the tree's root system will not be able to cope with the increased traffic.
A judicial review is when a case is heard by a high court judge, who decides whether a project continues on as is or if the council must notify the public and allow for submissions.
FreshChoice co-owner Chris Ward said they were technically an "interested bystander" regarding the challenge to the resource consent.
"The council have followed their process, which they believe is correct. As far as we're concerned, we're in possession of a legal document which entitles us to proceed."
With regards to the "palaver" over the sign, he said what the heritage group did not appreciate was the amount of work done "in the background" to recognise Greytown's heritage look, and the sign is "highly likely" to be a different design once finalised.
"They [The Friends] have failed to come and talk to me about it."